$8.$ Design a cereal comparator which compares two $6-$bit numbers, A and B$.$ The numbers are read from two one$/$ bit inputs, Ai and Bi$,$ one bit at a time, and the bits are arranged in decreasing order of significance. The final state should continuously output $0$ if A $>=$ B and $1$ if is A $<$ B

a$)$ give an ASM chart for the circuit$$

b$)$ Assuming the control module has been designed correctly, sketch the data path. For any modules required to implement status signals, just explain how they work, no need to implement them explicitly.$$

c$)$ with two of these comparators, and a single nor gate, explain how to design a circuit with three outputs: one true when A is lesser than B$,$ one true when A is greater than B$,$ and one true when A is equal to B$.$